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New forms of the Cauchy operator and some of their applications

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Abstract

In this paper, we first construct the Cauchy q-shift operator T(a, b;D xy ) and the Cauchy q-difference operator L(a, b; θ xy ). We then apply these operators in order to represent and investigate some new families of q-polynomials which are defined in this paper. We derive some q-identities such as generating functions, symmetry properties and Rogers-type formulas for these q-polynomials. We also give an application for the q-exponential operator R(bD q ).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3R4, Canada

    H. M. Srivastava

  2. China Medical University, Taichung Taiwan, 40402, Republic of China

    H. M. Srivastava

  3. Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq

    M. A. Abdlhusein

Authors
  1. H. M. Srivastava
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  2. M. A. Abdlhusein
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Correspondence to H. M. Srivastava.

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Srivastava, H.M., Abdlhusein, M.A. New forms of the Cauchy operator and some of their applications. Russ. J. Math. Phys. 23, 124–134 (2016). https://doi.org/10.1134/S1061920816010118

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  • DOI: https://doi.org/10.1134/S1061920816010118

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